Problem: Divide the polynomials.
Solution: Usually, there are many different ways to divide polynomials. Here, we will use the method of polynomial long division. Notice the numerator is missing a $1^{\text{st}}$ degree term. Let's add it as $0x$. $\begin{array}{r} x-\phantom{1}5 \\ x+5|\overline{x^2+0x-28} \\ \mathllap{-(}\underline{x^2+5x\phantom{-28}\rlap )} \\ -5x-28 \\ \mathllap{-(}\underline{-5x-25\rlap )} \\ -3 \end{array}$ We get that the quotient is $x-5$ and the remainder is $-3$, and therefore: $\dfrac{x^2-28}{x+5}=x-5-\dfrac{3}{x+5}$ [I want to see a different way of performing the division.]